Generally, in a multiple input, multiple output (MIMO) wireless communications system, it is beneficial for a transmitter to have some knowledge of channel state information of a communications channel between itself and a receiver. One form of channel state information, as implemented in technical standards such as the Third Generation Partnership Project (3GPP) Long Term Evolution (LTE), is a combination of a precoding matrix index (PMI), a channel quality index (CQI) and a rank indicator (RI).
Typically, channel state information may be provided in the form of feedback from the receiver. However, due to overall bandwidth utilization issues, a feedback channel usually has limited bandwidth as well as a low reliable transmission rate. Therefore, the channel state information may need to be quantized or otherwise reduced in size prior to being feedback. Predefined codebooks containing codewords at both the transmitter and the receiver is a commonly used technique to reduce feedback channel overhead by allowing the receiver to feedback an index to a codeword in the codebook rather than the codeword itself.
In multi-cell downlink transmissions, multiple base stations may simultaneously transmit to a single mobile station. In this situation, an effective number of transmit antennas may easily exceed four, which is usually the number of transmit antennas used in the design of codebooks in many technical standards. Furthermore, there is no standardized method for quantizing the PMI for a large number of transmit antennas.
Some of the technical standards also allow the use of relay nodes (RN). These technical standards may allow the RN and a base station to simultaneously transmit to a receiver. The receiver may need to quantize a joint communications channel (a communications channel between the RN and itself and a communications channel between the base station and itself), which may also exceed four transmit antennas.
Furthermore, transmissions from different transmission points may experience different losses, such as path loss, fading, shadowing, and so forth, which may mean that transmissions originally transmitted at substantially the same power level may arrive at their destinations at different energy levels. For example, a transmission from a distant transmission point may arrive at a destination at a lower energy level than a transmission made from a near transmission point. Therefore, different components of beamforming vectors may have different energies.